A rampage by Palestinian gunmen earlier this week underscores the challenges faced by Palestinian President Mahmoud Abbas. Mr. Abbas will be judged by Israel and the world on his ability to bring peace to the West Bank and Gaza Strip. Only if he succeeds will peace negotiations and the steps toward the realization of a Palestinian state continue.

But forging a peace requires him to gain control of the fractious Palestinian security bureaucracy and to muzzle extremists that have traditionally had a free hand to do as they please. It is still unclear whether any Palestinian leader has the strength and the courage to face down the militants.

For Israel, there is a simple litmus test that it applies to its negotiating partner: The Palestinian leadership must halt terror attacks by Palestinians against Israeli targets. Only then will Israelis know that Palestinians are serious about living in peace with them. Only then will the Israeli government be ready to move forward with peace negotiations and the creation of a Palestinian state.

Former Palestinian leader Yasser Arafat talked peace, but he refused, or was unable, to crack down on militants who regularly launched terror attacks against Israel. For Israelis, this was proof of his duplicity. For them, Arafat remained a guerrilla committed to the destruction of Israel.

Arafat’s successor, Mr. Abbas, has said that Palestinians must be prepared to abandon the armed struggle, and he has taken steps to translate those words into action. He has negotiated a truce with several armed factions and has been trying to extend it to others.

Thus far, Mr. Abbas has used persuasion to get the militants to put down their guns. Israeli critics complain that he should be more forceful, but given the divisions among Palestinians, their security forces and the militants themselves, the go-slow approach is the most that can be hoped for right now. Israeli efforts to crush the militants have crippled the Palestinian security forces, too.

Mr. Abbas may be losing patience. Earlier this week, Palestinian officials ordered several militants who had been living in the Palestinian headquarters compound to either give up their weapons or leave. They had been in the compound for several years. Wanted by Israel, they had been given shelter by Arafat. Rather than give up their weapons, the men went on a rampage, firing shots in the headquarters and starting fires.

It is unclear whether the men were guerrillas, common criminals or members of the Palestinian security forces who were worried that giving up their weapons would mean the loss of their livelihoods. They may have comprised elements of each: Fatah members who served in the security forces and who engaged in thuggery and criminal behavior on the side.

Firing shots in the Palestinian compound crossed “a red line.” Mr. Abbas demanded that the men be disarmed. That demand was quickly scaled back after the violence. A deal has been worked out that allows the militants to keep their weapons. According to some reports, fear that the militants might attack the Palestinian leadership itself had been one concern.

The retreat prompted the head of Palestinian intelligence on the West Bank to resign. The situation underscores the fact that the militants are not tools or cards to be used against the Israelis, but rather a threat to law and order within Palestinian territory. As has become apparent in other places and circumstances, the idea that militants can be harnessed to someone else’s political agenda is a delusion. They are loyal to no cause but their own.

In an attempt to show its good faith to the new leadership, Israel had agreed to hand over five West Bank towns to the Palestinians. The Israelis halted the process after two were given back, saying they would not proceed further until the Palestinians disarmed hundreds of militants wanted by Israel.

While welcome, Palestinian progress made thus far has exposed divisions. With territory comes power, and with the Palestinian infrastructure damaged after four years of intifada, power flows from the barrel of a gun. This is why the Palestinians are reluctant to disarm: For many, especially the young, their weapons are their only guarantee of respect, authority and a livelihood.

As Palestinians fight among each other, the most important question is whether Mr. Abbas has the power and authority to punish them for crossing his “red lines.”

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